An alternative approach to inverse \(\mathcal {Z}\)-transform of rational functions

The inverse -transform is a fundamental tool in the analysis of discrete-time signals, enabling the recovery of time-domain representations from frequency-domain data. Traditional methods for computing the inverse -transform of rational functions, such as long division, contour integration, and partial fraction expansion, often involve complex calculations and may not handle all cases efficiently. This article presents a novel method that addresses these limitations by utilizing conventional partial fraction expansion over real numbers, thereby simplifying the process and reducing the likelihood of errors. The proposed technique is particularly advantageous for handling complex poles and avoids the need for additional algebraic manipulations. Through illustrative examples and comparisons with existing methods, the article demonstrates the versatility and efficiency of the new approach. The supplementary material provides implementations of all discussed methods, facilitating a comprehensive understanding and practical application of the proposed technique.